The Marginal Cost of Public Funds is the Ratio of Mean Income to median Income
The marginal cost of public funds is the equilibrium price at the intersection of the appropriately-defined demand curve for and the supply curve of public expenditure. In a world with identical people and with no excess burden of taxation, that price would have to be 1. Otherwise the median voter's choice of a demogrant - or of its opposite, a head tax - fixes the marginal cost of public funds at the ratio of the mean income to the median income. A proof of this assertion is presented not for its realism, but because it calls attention to the interaction of the different influences upon the marginal cost of public funds.
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